When any term in this sequence is divided by the previous term, the result is always the same.
3, -6, 12, -24, ...
What is the 7th term of this sequence?
f 96 g -96 h 192 j -192
The common ratio between any two consecutive terms in the sequence is -2. Therefore, the 7th term can be found by multiplying the 6th term (-48) by -2:
-48 * (-2) = 96
So the answer is (f) 96.
Tn = Tn-1 * -2
= 3 * (-2)^(n-1)
looks like
if n = 1 , T1 = 3 *(-2)^0 = 3*1 = 2
if n = 2, T2 = 3 * ( -2)^1 = 3 * -2 = -6
if n = 3, T3 = 3 * (-2)^2 = 3 * 4 = 12
etc
if n = 7, T7 = 3 (-2)^6 = 3 * 64 = 192
( You found T6 I think )
You are correct, thank you for pointing that out! T6 would be -48 and multiplying it by -2 would give the 7th term to be 96.
ah well, continuing
if n = 4, T4 = 3 * (-2)^3 = 3 * -8 = -24
if n = 5, T5 = 3 * (-2)^4 = 3 * 16 = 48
if n = 6, T6 = 3 * (-2)^5 = 3 * -32 = -96
if n = 7, T7 = 3 * (-2)^6 = 3 * 64 = 192 <========
Yes, you are correct! Thank you for completing the sequence. The 7th term is indeed (h) 192.
To find the 7th term of this sequence, we first need to determine the common ratio between each term. The common ratio is found by dividing any term in the sequence by the previous term.
Let's calculate the common ratio:
-6 divided by 3 = -2
12 divided by -6 = -2
-24 divided by 12 = -2
Since the result is always -2, we know that the common ratio is -2.
Now, we can find the 7th term by multiplying the 6th term by the common ratio (-2).
6th term: -24
Common ratio: -2
7th term = 6th term * common ratio
7th term = -24 * -2
7th term = 48
Therefore, the 7th term of this sequence is 48.